What is physical? Something you can touch and feel for example. Mechanical time would be the clock (watch). It refers to the rotation of our planet. But what would be the physical time? Energy and forces, the reaction of 2 or more different existing things. Some call that matter. Chemical reaction is the best example for motion. So the time everyone is talking about is actually the mechanical time. And physical time would be motion, but that's not time. You've got motion when 2 or more different things react with each other.

Is time travel possible? What time? There's only mechanical time. Physical is motion. Time travel to the past is impossible, because the opposite of motion is no motion (standstill). And traveling to the future could be possible if you could slow down the reaction of the things that your body consists of. Everything around you will move fast, you stay young, and everyone else around you will be old.
Move as fast as Superman: If you could accelerate the reaction of the things that your body consists of, you would be able to think and move faster, but also age faster than everyone else around you.